Seismic data acquisition and processing techniques are used to generate a profile (image) of a geophysical structure (subsurface) of the strata underlying the land surface or seafloor. Among other things, seismic data acquisition involves the generation of acoustic waves and the collection of reflected/refracted versions of those acoustic waves to generate the image. This image does not necessarily provide an accurate location for oil and gas reservoirs, but it may suggest, to those trained in the field, the presence or absence of oil and/or gas reservoirs. Thus, providing an improved image of the subsurface in a shorter period of time is an ongoing process in the field of seismic surveying.
The signals recorded by seismic receivers vary in time, having energy peaks that may correspond to reflectors between layers in the subsurface being imaged. In reality, and referencing marine seismic acquisition as an example, since the sea floor and the air/water are highly reflective, some of the peaks correspond to multiple reflections or spurious reflections that should be eliminated before the geophysical structure can be correctly imaged. So-called primary waves suffer only one reflection of the acoustic wave generated by a source to the receiver, i.e., a reflection from an interface between layers of the subsurface. Waves other than primary waves are known as multiples. A surface multiple signal, i.e., a signal generated when an acoustic wave strikes the water's surface, is one example of a multiple, however there are other ways for multiples to be generated. Surface multiples can travel back down to the receivers and be recorded as ghosts. Multiples hinder the interpretation of the geology beneath the ocean floor, and thus they are, in essence, noise for most seismic data processing purposes. It is therefore typically desirable to eliminate them and/or substantially reduce and/or eliminate their influence in signal processing of the other reflected signals so as to correctly ascertain the presence (or the absence) of underground/underwater hydrocarbon deposits.
Accordingly, it will be appreciated by those skilled in the art that, in order to improve seismic images, multiples attenuation plays an important role in the pre-processing of seismic data. Generally, the process of multiples attenuation involves two steps: 1) the prediction of multiples; and 2) the separation of the primaries and multiples. Over the past two decades, considerable effort has been dedicated to improving the capability to predict multiples.
For example, methods such as Surface Related Multiple Elimination (SRME) have become routine tools for effective multiple prediction of long-period multiples. In conjunction, short-period multiples generated by a shallow sea floor and internal multiples generated by subsurface interfaces of high impedance contrast have also attracted the attention of the research community, e.g., research by N. Hargreaves in his 2006 article entitled “Surface Multiple Attenuation in Shallow Water and the Construction of Primaries from Multiples,” published in 76th Annual International Meeting, SEG, Expanded Abstracts, pages 2689-2693 and incorporated herein by reference, by P. Wang, H. Jin, S. Xu and Y. Zhang in their 2011 article entitled “Model-Based Water-Layer Demultiple,” published in 81st Annual International Meeting, SEG and incorporated herein by reference and by M. Wang, B. Hung and K. Xin in their 2012 article entitled “Application of Inverse Scattering Series Method for Internal Multiple Attenuation: A Case Study,” published in ASEG Extended Abstract and incorporated herein by reference.
Equally as important as advancements in multiples prediction, is the development of an effective strategy for separating multiples from primaries. One of the most widely accepted strategies for multiple/primary separation is the L2-Norm based least-square separation method (LS) as described by D. J. Verschuur and A. J. Berkhout in their 1997 article entitled “Estimation of Multiple Scattering by Iterative Inversion, Part II: Practical Aspects and Examples,” published in Geophysics, 62, pages 1596-1611 and incorporated herein by reference. The LS method allows for a degree of inaccuracy in the prediction of the multiples, i.e., comprising errors in the travel time, the amplitude and the spectrum. However, a compromise is required between the preservation of the primaries and the attenuation of the multiples, especially in locations where primary and multiple events either cross each other or overlap.
As a result of the compromise between preservation of primaries and attenuation of multiples increasing attention has been devoted to other separation methods such as curvelet-based separation methods. Curvelet-based separation methods have the advantage of minimizing the damage to the primary events based on the compatible nature of the curvelet transform to seismic data, as described by F. J. Herrmann, D. Wang and D. J. Verschuur in their 2008 article entitled “Adaptive Curvelet-Domain Primary-Multiple Separation,” published in Geophysics, 73, pages 17-21 and incorporated herein by reference.
Unfortunately, symptomatic of the various implementations of the curvelet domain separation approaches, the non-adaptive implementations can encounter a problem of numerical divergence if the predicted multiples vary from the actual multiples in the seismic data and the adaptive implementations either only correct for limited misalignment between the predicted multiples and the actual multiples or incur high computational costs based on the use of curvelet matching filtering as described by R. Saab, D. Wang, Ö. Yιlmaz and F. J. Herrmann in their 2007 article entitled “Curvelet-Based Primary-Multiple Separation from a Bayesian Perspective,” published in The 77th Annual International Meeting, SEG and incorporated herein by reference and by R. Neelamani, A. Baumstein, and W. S. Ross in their 2010 article entitled “Adaptive Subtraction Using Complex-Valued Curvelet Transforms,” published in Geophysics, 75, pages 51-60 and incorporated herein by reference.
Accordingly, it would be desirable to provide systems and methods that avoid the afore-described problems and drawbacks associated with the improvement of seismic images based on multiple prediction and multiple/primary separation by converging curvelet approaches.